Experience based premium rate discounts using Tweedie’s and Tobit’s regression models: an application to crop insurance.
Prof. José Luis Vilar Zanón- Dept. Financial & Actuarial Economics and Statistics - Universidad Complutense de Madrid
Abstract
In Actuarial Mathematics, the concept of Bonus-Malus System (BMS) is a very important one. It allows the design of experience based discount premium systems that we find very often in the insurance markets, particularly in automobile insurance. The foundation of the classical BMS is the hypothesis that the individual policy risk is modeled by means of a single parameter, the mean number of claims. This is supposed to be a random variable distributed by a structure function.
Yet this hypothesis is hard to assume in other insurance markets. For instance, this is the case in crop or agricultural insurance where it is not realistic any more. In addition, the occurrence of high losses associated to meteorological events can result in a malfunction of the classical BMS, giving premium increases not commercially affordable or premiums insufficiency. Yet the application of classical BMS is a common practice in many contries of the EU.
We explain how it is still possible to build up an experience based premium rate discount system applied to crop insurance, able to deal with adverse year’s losses and reaching the financial equilibrium. We will also explain how we can measure the efficiency of the system.
Our methodology builds up a “mean model” able to buffer the adverse years losses. At the yearly stage, it is implemented through two differentregression techniques. The first one is the normal censored regression or Tobit’s model. The second one is Tweedie’s generalized linear model that gives a natural actuarial interpretation of the high number of zeroes contained in the data sample.
We apply this “mean model” methodology to a Spanish data set taken from a business line in crop insurance (table grapes) during the years 2012-2016.